Either should be fine but first I would ask how well you know the person. If you know them well it would probably be viewed as slightly joking but friendly. If you don’t know them very well it could possibly be taken as being a little sarcastic. Maybe that's just how I would see it, so wait and see what others have to say.
Personally, I would write: Is it possible that you could spare me some (of your) time?

I agree with Helicopta and think that the use of "precious" may sound a bit sarcastic.

I would simply say, "I appreciate your valuable time."

I understand that you're trying to be very polite, but I wouldn't ask someone to "spare" me time. The best way to show that you do appreciate someone's time is to word your letter succinctly (without a lot of extra words). Get right to the point.

I agree with Helicopta and think that the use of "precious" may sound a bit sarcastic.

I would simply say, "I appreciate your valuable time." .

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I'm afraid that using 'valuable' sounds equally sarcastic as 'precious' to me (maybe it's just me). I think 'would' or 'could' should be in there somewhere as tstrmkll is asking someone to give up their time to help him/her, not thanking them for having done so.

modgirl said:

I understand that you're trying to be very polite, but I wouldn't ask someone to "spare" me time. The best way to show that you do appreciate someone's time is to word your letter succinctly (without a lot of extra words). Get right to the point.

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Maybe 'spare' is a little too informal. What about "Your time would be greatly appreciated" or "I would very much appreciate your time"?

Originally posted by Helicopta
I'm afraid that using 'valuable' sounds equally sarcastic as 'precious' to me (maybe it's just me).

Originally posted by Modgirl
I agree with Helicopta and think that the use of "precious" may sound a bit sarcastic.

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I don't think it's a matter of sarcasm, so much as it is a matter of appropriate context.

From a business perspective, I think one would hear that time is "valuable." Afterall, to a corporate executive, time = money.

To a mother with a growing child, time spent with that child is "precious." In this case, precious carries with it an idea of emotional value, not monetary value.

In asking someone to meet with you, I agree with modgirl in that I would be polite, but keep the letter as to-the-point as possible. Afterall, if they consider their time to be valuable, they do not have much to ready wordy letters.

I would keep your request simple, and put it in the form of a question. I would also state your specific intent and a suggested amount of time the meeting might take.

If you can give us a bit more context, we might be able to help formulate a paragraph that would be deemed appropriate.

I have bought a new car and the salesperson was very kind and she did her work very well, and I am sending email to her. I would like to know when they are able to deliver the car and the same email to ask more questions about the car. I know that this is her job to give those answers but I would like to put little bit more than short questions. Probably time is money to her.

Thank you for taking the time to work with me on selecting my new <name of car here.> You really went out of your way to ensure my car buying experience was a pleasant one.

Per our discussion last <day>, we discussed several issues, including a probable delivery date for the vehicle. I would appreciate it if you could confirm the exact date of delivery so I may make appropriate arrangments to receive it.

I also have some other questions: (Ask your questions here).

1. question No. 1
2. question No. 2
3. question No. 3

Thank you very much for your prompt and courteous attention to this matter.